Java Program to Sort an array in wave form

Given an unsorted array of integers, sort the array into a wave-like array. An array ‘arr[0..n-1]’ is sorted in wave form if arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4] >= …..

Examples: 

 Input:  arr[] = {10, 5, 6, 3, 2, 20, 100, 80}
 Output: arr[] = {10, 5, 6, 2, 20, 3, 100, 80} OR
                 {20, 5, 10, 2, 80, 6, 100, 3} OR
                 any other array that is in wave form

 Input:  arr[] = {20, 10, 8, 6, 4, 2}
 Output: arr[] = {20, 8, 10, 4, 6, 2} OR
                 {10, 8, 20, 2, 6, 4} OR
                 any other array that is in wave form

 Input:  arr[] = {2, 4, 6, 8, 10, 20}
 Output: arr[] = {4, 2, 8, 6, 20, 10} OR
                 any other array that is in wave form

 Input:  arr[] = {3, 6, 5, 10, 7, 20}
 Output: arr[] = {6, 3, 10, 5, 20, 7} OR
                 any other array that is in wave form
 

A Simple Solution is to use sorting. First sort the input array, then swap all adjacent elements.
For example, let the input array be {3, 6, 5, 10, 7, 20}. After sorting, we get {3, 5, 6, 7, 10, 20}. After swapping adjacent elements, we get {5, 3, 7, 6, 20, 10}. 

Below are implementations of this simple approach. 

Java

// Java implementation of naive method for sorting
// an array in wave form.
import java.util.*;

class SortWave
{
    // A utility method to swap two numbers.
    void swap(int arr[], int a, int b)
    {
        int temp = arr[a];
        arr[a] = arr[b];
        arr[b] = temp;
    }

    // This function sorts arr[0..n-1] in wave form, i.e.,
    // arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4]..
    void sortInWave(int arr[], int n)
    {
        // Sort the input array
        Arrays.sort(arr);

        // Swap adjacent elements
        for (int i=0; i<n-1; i += 2)
            swap(arr, i, i+1);
    }

    // Driver method
    public static void main(String args[])
    {
        SortWave ob = new SortWave();
        int arr[] = {10, 90, 49, 2, 1, 5, 23};
        int n = arr.length;
        ob.sortInWave(arr, n);
        for (int i : arr)
            System.out.print(i + " ");
    }
}
/*This code is contributed by Rajat Mishra*/

Output

2 1 10 5 49 23 90 

Time complexity: O(n Log n), if a O(nLogn) sorting algorithm like Merge Sort, Heap Sort, .. etc is used.
Auxiliary Space: O(1)

Another approach: 
This can be done in O(n) time by doing a single traversal of given array. The idea is based on the fact that if we make sure that all even-positioned (at index 0, 2, 4, ..) elements are greater than their adjacent odd elements, we don’t need to worry about odd positioned elements.

The following are simple steps. 

• Traverse all even positioned elements of input array, and do following. 
  • If current element is smaller than previous odd element, swap previous and current. 
  • If current element is smaller than next odd element, swap next and current.

Below are implementations of the above simple algorithm. 

Java

// A O(n) Java program to sort an input array in wave form
import java.util.*;

class SortWave
{
    // A utility method to swap two numbers.
    void swap(int arr[], int a, int b)
    {
        int temp = arr[a];
        arr[a] = arr[b];
        arr[b] = temp;
    }

    // This function sorts arr[0..n-1] in wave form, i.e.,
    // arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4]....
    void sortInWave(int arr[], int n)
    {
        // Traverse all even elements
        for (int i = 0; i < n; i+=2)
        {
            // If current even element is smaller
            // than previous
            if (i>0 && arr[i-1] > arr[i] )
                swap(arr, i-1, i);

            // If current even element is smaller
            // than next
            if (i<n-1 && arr[i] < arr[i+1] )
                swap(arr, i, i + 1);
        }
    }

    // Driver program to test above function
    public static void main(String args[])
    {
        SortWave ob = new SortWave();
        int arr[] = {10, 90, 49, 2, 1, 5, 23};
        int n = arr.length;
        ob.sortInWave(arr, n);
        for (int i : arr)
            System.out.print(i+" ");
    }
}
/*This code is contributed by Rajat Mishra*/

Output

90 10 49 1 5 2 23 

Time complexity: O(n)
Auxiliary space: O(1)

Please refer complete article on Sort an array in wave form for more details!